What are ways to get approved with no rental history? Most apartment buildings don't rent to young people with no rental history or at least those are all the ones that I've seen so far.Yes, you can rent an apartment with no rental history. But you're going to have to provide the paperwork that proves you can afford it. List Reputable References. It is possible to submit an application without having rented in the past. On the Residence History step, enter your current address, and set dates. It is non-refundable whether or not the application is approved. You must carry out tenant background checks on all rental applications for your investment property. If you don't, you could end up with bad tenants.